To interpret the slope and the y-intercept of the linear model, let’s analyze the information provided:
The points you mentioned include the y-intercept (0,0) and the ordered pair (9,42). This suggests that at 0 months, the average weight of a dog is 0 pounds, and at 9 months, the average weight is 42 pounds. We can calculate the slope of the line using these two points.
First, we use the slope formula, which is:
\[ \text{slope (m)} = \frac{y_2 - y_1}{x_2 - x_1} \]
In this case, we can take:
- \((x_1, y_1) = (0, 0)\)
- \((x_2, y_2) = (9, 42)\)
Now we plug these values into the slope formula:
\[ m = \frac{42 - 0}{9 - 0} = \frac{42}{9} \approx 4.67 \]
So, the slope (rounded to the nearest hundredth) is approximately 4.67.
Interpretation:
- The slope of 4.67 means that "every month, a dog averages a gain of approximately 4.67 pounds."
- The y-intercept (0,0) indicates that at birth (0 months), the average weight of a dog is 0 pounds.
Among the response options you provided, the correct interpretation is:
Every month, a dog averages a gain of 4.67 pounds and weighs 0 pounds at birth.